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Water 2019, 11(4), 707; https://doi.org/10.3390/w11040707

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

1
Department of Geological Sciences, University of Alabama, Tuscaloosa, AL 35487, USA
2
College of Mechanics and Materials, Hohai University, Nanjing 210098, China
3
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
4
Guangdong Provincial Key Laboratory of Soil and Groundwater Pollution Control, School of Environmental Science & Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
5
Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89119, USA
*
Author to whom correspondence should be addressed.
Received: 16 February 2019 / Revised: 24 March 2019 / Accepted: 26 March 2019 / Published: 5 April 2019
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Abstract

Hydrological extremes in the water cycle can significantly affect surface water engineering design, and represents the high-impact response of surface water and groundwater systems to climate change. Statistical analysis of these extreme events provides a convenient way to interpret the nature of, and interaction between, components of the water cycle. This study applies three probability density functions (PDFs), Gumbel, stable, and stretched Gaussian distributions, to capture the distribution of extremes and the full-time series of storm properties (storm duration, intensity, total precipitation, and inter-storm period), stream discharge, lake stage, and groundwater head values observed in the Lake Tuscaloosa watershed, Alabama, USA. To quantify the potentially non-stationary statistics of hydrological extremes, the time-scale local Hurst exponent (TSLHE) was also calculated for the time series data recording both the surface and subsurface hydrological processes. First, results showed that storm duration was most closely related to groundwater recharge compared to the other storm properties, while intensity also had a close relationship with recharge. These relationships were likely due to the effects of oversaturation and overland flow in extreme total precipitation storms. Second, the surface water and groundwater series were persistent according to the TSLHE values, because they were relatively slow evolving systems, while storm properties were anti-persistent since they were rapidly evolving in time. Third, the stretched Gaussian distribution was the most effective PDF to capture the distribution of surface and subsurface hydrological extremes, since this distribution can capture the broad transition from a Gaussian distribution to a power-law one. View Full-Text
Keywords: statistical analysis; hydrological extremes; stretched Gaussian distribution; Hurst exponent statistical analysis; hydrological extremes; stretched Gaussian distribution; Hurst exponent
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Dawley, S.; Zhang, Y.; Liu, X.; Jiang, P.; Tick, G.R.; Sun, H.; Zheng, C.; Chen, L. Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation. Water 2019, 11, 707.

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